Modelling and Subtracting Diffuse Cluster Light in JWST Images: A Relation between the Spatial Distribution of Globular Clusters, Dwarf Galaxies, and Intracluster Light in the Lensing Cluster SMACS 0723

We present a methodology for modeling and removing light from cluster galaxies and intracluster light (ICL) from $James\ Webb\ Space\ Telescope$ ($JWST$) images of gravitational lensing clusters. We apply our method to Webb's First Deep Field the SMACS 0723 Early Release Observations and use the ICL subtracted images to select a sample of globular clusters (GCs) and dwarf galaxies within the cluster. We compare the spatial distributions of these two samples with our models of the galaxy and ICL light, finding significant similarity. Specifically we find that GCs trace the diffuse ICL, while dwarf galaxies are centrally concentrated near the cluster center We quantify the relationship between the surface density of compact sources and total cluster light, demonstrating a significant, tight correlation. We repeat our methodology and compare distributions of GCs with dark matter surface density and find a comparable result. Our findings suggest a common origin for GCs and diffuse ICL, with stripping from massive galaxies as they merge with the cluster being a plausible scenario.